Determining If a Relation Is a Function

Get ready to test your logic and pattern skills with Determining If a Relation Is a Function! This engaging activity helps you explore what makes a relation a function — a special kind of relationship where each input (x) is paired with exactly one output (y). You’ll use tables, mappings, sets, and graphs to decide if a relation passes the “function test.”

You’ll begin by reviewing the basic rule: every input can have only one output. You’ll look at examples like {(1, 3), (2, 5), (3, 7)} — which is a function — and {(2, 4), (2, 6), (3, 8)} — which is not! Each example helps you recognize that repeated x-values with different y-values mean the relation fails to be a function.

Next, you’ll analyze mappings, tables, and graphs to apply this rule visually. You’ll use the Vertical Line Test for graphs — if any vertical line touches a graph more than once, it’s not a function. These checks help you connect algebraic concepts to visuals, reinforcing your understanding through clear, hands-on examples.